Year: 2025
Type: preprint
Abstract: The aim of this paper is to investigate the fractional combinatorial Calabi flow for hyperbolic bordered surfaces. By Lyapunov theory, it is proved that the flow exists for all time and converges exponentially to a conformal factor that generates a hyperbolic surface whose lengths of boundary components are prescribed positive numbers. Furthermore, a generalized combinatorial Yamabe flow is introduced in the same geometry setting, with the long time existence and convergence established. This result yields an algorithm for searching bordered surfaces, which may accelerate convergence speed.
Source: arXiv (Cornell University)
Authors: Li, Shengyu, Wang, Zhi-Gang
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416052572
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